Đáp án+Giải thích các bước giải:
`a)A=(30^2+28^2+26^2+.....+4^2+2^2)-(29^2+27^2+...++3^2+1^2)`
`=(30^2-29^2)+(28^2-27^2)+(26^2-25^2)+....+(4^2-3^2)+(2^2-1^2)`
`=(30-29)(30+29)+(28-27)(28+27)+(26-25)(26+25)+....+(4-3)(4+3)+(2-1)(2+1)`
`=59+55+51+....+7+3`
`text{số số hạng của dãy trên là:}`
`(59-3):4+1=15`(số hạng)
`A=(59+3).15:2`
`=465`
`b)B=12(5^2+1)(5^4+1)(5^8+1).....(5^{128}+1)+1/2(5^{256}-1)`
`2B=24(5^2+1)(5^4+1)......(5^{128}+1)+(5^{256}-1)`
`=(5^2-1)(5^2+1)(5^4+1)......(5^{128}+1)+(5^{256}-1)`
`=(5^4-1)(5^4+1)........(5^{128}+1)+(5^{256}-1)`
`=(5^8-1).........(5^{128}+1)+(5^{256}-1)`
`..................................................................................`
`=(5^{128}-1)(5^{128)+1)+(5^{256}-1)`
`=5^{256}-1+5^{256}-1`
`=2(5^{256}-1)`
⇒`B=5^{256}-1`
`c)C=(3^2+1)(3^4+1)(3^8+1)-3^{16}/8`
`8C=8(3^2+1)(3^4+1)(3^8+1)-3^{16}`
`=(3^2-1)(3^2+1)(3^4+1)(3^8+1)-3^{16}`
`=(3^4-1)(3^4+1)(3^8+1)-3^{16}`
`=(3^8-1)(3^8+1)-3^{16}`
`=3^{16}-1-3^{16}`
`=-1`
⇒`C=-1/8`
`d){[(3^2)^2]^2}^2-2(3+1)(3^2+1)(3^4+1)(3^8+1)`
`={[3^4]^2}^2-(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)`
`={3^8}^2-(3^2-1)(3^2+1)(3^4+1)(3^8+1)`
`=3^{16}-(3^4-1)(3^4+1)(3^8+1)`
`=3^{16}-(3^8-1)(3^8+1)`
`=3^{16}-(3^{16}-1)`
`=3^{16}-3^{16}+1`
`=1`
`____________________`
Chúc bạn học tốt!!!!
`#Rùa~ ~ ~`
